Toward Trainability of Deep Quantum Neural Networks

• URL: http://arxiv.org/abs/2112.15002v2
• Date: Mon, 26 Sep 2022 10:34:24 GMT
• Title: Toward Trainability of Deep Quantum Neural Networks
• Authors: Kaining Zhang and Min-Hsiu Hsieh and Liu Liu and Dacheng Tao
• Abstract summary: Quantum Neural Networks (QNNs) with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase. We provide the first viable solution to the vanishing gradient problem for deep QNNs with theoretical guarantees.
• Score: 87.04438831673063
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum Neural Networks (QNNs) with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase. This result leads to a general belief that a deep QNN will not be feasible. In this work, we provide the first viable solution to the vanishing gradient problem for deep QNNs with theoretical guarantees. Specifically, we prove that for circuits with controlled-layer architectures, the expectation of the gradient norm can be lower bounded by a value that is independent of the qubit number and the circuit depth. Our results follow from a careful analysis of the gradient behaviour on parameter space consisting of rotation angles, as employed in almost any QNNs, instead of relying on impractical 2-design assumptions. We explicitly construct examples where only our QNNs are trainable and converge, while others in comparison cannot.

Related papers

• Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients [51.82488018573326]
  We present QP-SBGD, a novel layer-wise optimiser tailored towards training neural networks with binary weights. BNNs reduce the computational requirements and energy consumption of deep learning models with minimal loss in accuracy. Our algorithm is implemented layer-wise, making it suitable to train larger networks on resource-limited quantum hardware.
  arXiv  Detail & Related papers  (2023-10-23T17:32:38Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Theory of overparametrization in quantum neural networks [0.0]
  We rigorously analyze the overparametrization phenomenon in Quantum Neural Networks (QNNs) with periodic structure. Our results show that the dimension of the Lie algebra obtained from the generators of the QNN is an upper bound for $M_c$. We then connect the notion of overparametrization to the QNN capacity, so that when a QNN is overparametrized, its capacity achieves its maximum possible value.
  arXiv  Detail & Related papers  (2021-09-23T22:39:48Z)
• Toward Trainability of Quantum Neural Networks [87.04438831673063]
  Quantum Neural Networks (QNNs) have been proposed as generalizations of classical neural networks to achieve the quantum speed-up. Serious bottlenecks exist for training QNNs due to the vanishing with gradient rate exponential to the input qubit number. We show that QNNs with tree tensor and step controlled structures for the application of binary classification. Simulations show faster convergent rates and better accuracy compared to QNNs with random structures.
  arXiv  Detail & Related papers  (2020-11-12T08:32:04Z)
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks [0.0]
  Quantum Convolutional Neural Networks (QCNNs) have been proposed. We rigorously analyze the gradient scaling for the parameters in the QCNN architecture.
  arXiv  Detail & Related papers  (2020-11-05T16:46:13Z)
• On the learnability of quantum neural networks [132.1981461292324]
  We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme. We show that if a concept can be efficiently learned by QNN, then it can also be effectively learned by QNN even with gate noise.
  arXiv  Detail & Related papers  (2020-07-24T06:34:34Z)
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks [0.8258451067861933]
  We analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs) We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits.
  arXiv  Detail & Related papers  (2020-05-26T00:59:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.